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(7) Discuss the stability of the fixed points for the map T(x) ,1x(1-2) for (8) Let x0€ 10, il be...
? (c) (2 pts) Let f(x) = 4xe-*. Find the fixed points and their stability. (d)...
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(c) (2 pts) Let f(x) = 4xe-*. Find the fixed points and their stability. (d) (2 pts) Let f(x) = 2.x2 – 3. Find the fixed points along with their stability and determine the 2-cycle along with its stability. (e) (2 pts) Let c > 0 and fc(x) = c (2 - V3x + 4). Find the interval of stability of 0.
Problem # 1: Let 3-1x< . f(x) 7x 0 x1 The Fourier series for f(x). (an...
Problem # 1: Let 3-1x< . f(x) 7x 0 x1 The Fourier series for f(x). (an cosx bsinx f(x) n1 is of the form f(x)Co (g1(n,x) + g2(n, x) ) n-1 (a) Find the value of co. (b) Find the function gi(n,x) (c) Find the function g(n, x) Problem #2 : Let f (x ) = 8-9x, - x< I Using the same notation as n Problem #1 above, (a) find the value of co- (b) find the function g1(n,x)....
Let f(x) = 10/x − x^2. Find all fixed points of f and determine 9 their...
Let f(x) = 10/x − x^2. Find all fixed points of f and determine
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their stability. To where are orbits under f attracted?
Problem 3: Let f(x) = 10x – x? Find all fixed points of f and determine their stability. To where are orbits under f attracted? Problem 4: Let f(x) = 10 x – 23. Find all fixed points of f and determine their stability. To where are orbits under f attracted?
7. Consider a family of maps f :R-R, where f(r)= 2+c, cE R. a) Let c 0. Find all the fixed points of f and analyze...
7. Consider a family of maps f :R-R, where f(r)= 2+c, cE R. a) Let c 0. Find all the fixed points of f and analyze the map by drawing a cobweb. Check stability of the fixed points b) Find and classify all the fixed points of f as a function of c. c) Find the values of c at which the fixed points bifurcate, and classify those bifurcations. d) For which values of c is there an attracting cycle...
Q4 [10 pts] Let x[n] = {1, Osns 7 10. 8 00 be a periodic signal...
Q4 [10 pts] Let x[n] = {1, Osns 7 10. 8 00 be a periodic signal with fundamental period N = 10 and Fourier series coefficients ag. Also, let 8[n] = x[n] - x[n - 1). (a) Show that g(n) has a fundamental period of 10. (b) Determine the Fourier series coefficients of g[n].
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï....
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï. Find the images of u Define the linear transformation T : R- and y 4 under = - T. T(M TM =
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï. Find the images of u Define the linear transformation T : R- and y 4 under = - T. T(M TM =
1.4. Let x[n] be a signal with x[n] = 0 for n < -2 and n...
1.4. Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each signal given below, determine the values of n for which it is guaranteed to be zero. (a) xịn - 3] (b) x[n+ 4] (c) x[-n] (d) x[-n+2] (e) x[-n-2] 1.5. Let x(t) be a signal with x(t) = 0 for t <3. For each signal given below, determine the values of t for which it is guaranteed to be zero....
1. Let T: R2 – R? be the map "reflection in the line y = x"—you...
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
Problem #6: Let 58 0 < t <a f(0) = -8 x<I< 27 and assume that...
Problem #6: Let 58 0 < t <a f(0) = -8 x<I< 27 and assume that when f(t) is extended to the negative t-axis in a periodic manner, the resulting function is even Consider the following differential equation. 3 d2x de 2 + 7x = $(1) Find a particular solution of the above differential equation of the form 00 00 Xp(1) git,n) P and enter the function g(t, ) into the answer box below.
8. Find the Fourier transform of the following signal. (5 points) x(0) 2 1 9. Determine...
8. Find the Fourier transform of the following signal. (5 points) x(0) 2 1 9. Determine whether or not the following signals are periodic, and if periodic, give their periods in seconds and frequency in hertz. a. X(t) = 12.8 Cos (320xt - . (3 points). b. x(n) = 11.6 Cos (3n). (3 points). 6. x(n) = 1.45 sinn). (3 points). 10. Determine whether or not the LTI systems with the following impulse responses are causal and stable. Note that...
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(c) (2 pts) Let f(x) = 4xe-*. Find the fixed points and their stability. (d) (2 pts) Let f(x) = 2.x2 – 3. Find the fixed points along with their stability and determine the 2-cycle along with its stability. (e) (2 pts) Let c > 0 and fc(x) = c (2 - V3x + 4). Find the interval of stability of 0.
Problem # 1: Let 3-1x< . f(x) 7x 0 x1 The Fourier series for f(x). (an cosx bsinx f(x) n1 is of the form f(x)Co (g1(n,x) + g2(n, x) ) n-1 (a) Find the value of co. (b) Find the function gi(n,x) (c) Find the function g(n, x) Problem #2 : Let f (x ) = 8-9x, - x< I Using the same notation as n Problem #1 above, (a) find the value of co- (b) find the function g1(n,x)....
Let f(x) = 10/x − x^2. Find all fixed points of f and determine
9
their stability. To where are orbits under f attracted?
Problem 3: Let f(x) = 10x – x? Find all fixed points of f and determine their stability. To where are orbits under f attracted? Problem 4: Let f(x) = 10 x – 23. Find all fixed points of f and determine their stability. To where are orbits under f attracted?
7. Consider a family of maps f :R-R, where f(r)= 2+c, cE R. a) Let c 0. Find all the fixed points of f and analyze the map by drawing a cobweb. Check stability of the fixed points b) Find and classify all the fixed points of f as a function of c. c) Find the values of c at which the fixed points bifurcate, and classify those bifurcations. d) For which values of c is there an attracting cycle...
Q4 [10 pts] Let x[n] = {1, Osns 7 10. 8 00 be a periodic signal with fundamental period N = 10 and Fourier series coefficients ag. Also, let 8[n] = x[n] - x[n - 1). (a) Show that g(n) has a fundamental period of 10. (b) Determine the Fourier series coefficients of g[n].
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï. Find the images of u Define the linear transformation T : R- and y 4 under = - T. T(M TM =
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï. Find the images of u Define the linear transformation T : R- and y 4 under = - T. T(M TM =
1.4. Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each signal given below, determine the values of n for which it is guaranteed to be zero. (a) xịn - 3] (b) x[n+ 4] (c) x[-n] (d) x[-n+2] (e) x[-n-2] 1.5. Let x(t) be a signal with x(t) = 0 for t <3. For each signal given below, determine the values of t for which it is guaranteed to be zero....
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
Problem #6: Let 58 0 < t <a f(0) = -8 x<I< 27 and assume that when f(t) is extended to the negative t-axis in a periodic manner, the resulting function is even Consider the following differential equation. 3 d2x de 2 + 7x = $(1) Find a particular solution of the above differential equation of the form 00 00 Xp(1) git,n) P and enter the function g(t, ) into the answer box below.
8. Find the Fourier transform of the following signal. (5 points) x(0) 2 1 9. Determine whether or not the following signals are periodic, and if periodic, give their periods in seconds and frequency in hertz. a. X(t) = 12.8 Cos (320xt - . (3 points). b. x(n) = 11.6 Cos (3n). (3 points). 6. x(n) = 1.45 sinn). (3 points). 10. Determine whether or not the LTI systems with the following impulse responses are causal and stable. Note that...
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